1,4,5-trigermabicyclo[2.1.0]pent-2-en-5-ylium: the isolable bishomocyclopropenylium ion containing a heavier group 14 element

The isolable bishomoaromatic cation containing a heavier Group 14 element, (2,3,5-deloc)-2-phenyl-1,4,5-tris(tri-tert-butylsilyl)-1,4,5-trigermabicyclo[2.1.0]pent-2-en-5-ylium TPFPB- (2+.TPFPB-; TPFPB- = tetrakis(pentafluorophenyl)borate) was synthesized by the reaction of 5-bromo-2-phenyl-1,4,5-tris(tri-tert-butylsilyl)-1,4,5-trigermabicyclo[2.1.0]pent-2-ene (1) with [Et3Si(benzene)]+.TPFPB- in benzene at room temperature. The characteristic bishomoaromatic structure was unambiguously determined by X-ray crystallographic analysis. NMR measurements on 2+.TPFPB- confirmed the nonclassical germyl cation structure in solution and showed strong shielding of homoconjugative carbon atoms. The bishomoaromaticity in 2+ was also investigated by theoretical calculations.     

Interpretation of the difference of optimal Mo density in MoS<Subscript>2</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and MoS<Subscript>2</Subscript>-TiO<Subscript>2</Subscript> HDS catalysts

The first part of this paper deals with the morphology of the MoS₂ phase and its oxide precursor, the MoO₃ phase, mainly from a geometrical point of view. After giving a brief review of the literature describing the structure of these compounds, Mo densities in both phases were calculated along various crystallographic planes. Further, using structural models recently proposed by others, Mo densities in MoS₂ were also calculated in the case of an epitactic growth on γ-Al₂O₃ and TiO₂ model surfaces. Then, the calculated Mo densities were compared with experimental results (Mo density when HDS activity is maximal) previously obtained for catalysts constituted of MoS₂ supported on a low SSA TiO₂, a high SSA TiO₂ and a conventional γ-alumina. It was suggested that either on alumina or titania the MoS₂ phase is growing as (100) MoS₂ planes. However, while on the alumina the optimal MoS₂ phase might be constituted of dispersed MoS₂ slabs covering only a part of the alumina surface (2.9–3.9 Mo atoms/nm²), on titania the optimal MoS₂ phase might be constituted of a uniform MoS₂ monolayer (5.2 atoms/nm² for the high SSA titania, which is equal to the Mo density of a perfect MoS₂ (100) plane). This difference may originate in the creation of a 'TiMoS' phase enhancing the S atoms mobility over Mo/TiO₂-sulfided catalysts. Indeed, while in the case of a γ-alumina carrier the active sites (labile S atoms) are located on the edge of MoS₂ slabs making the ratio Mo_edge/Mo_total a crucial parameter for the catalytic performances, in the case of a titania carrier the labile sulfur atoms might be statistically distributed all over the TiMoS active phase. Further, the higher Mo density observed over the high SSA titania (5.2 atoms/nm²) when compared to that over the low SSA titania (4.2 atoms/nm²) was supposedly due to the pH-swing method advantageously used to prepare the former carrier. Indeed, this method allows giving a solid with enhanced mechanical properties providing a good stability to the derived catalysts under experimental conditions. In addition, this TiO₂ carrier exhibits a great homogeneity, with a surface structure substantially uniform, which might be adequate for a long-range growth of (100) MoS₂ slabs.     

Matrix $$\mathcal {A}_p$$ Weights,Degenerate Sobolev Spaces,and Mappings of Finite Distortion

We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix \(\mathcal {A}_p\) weight. This class of weights was introduced by Nazarov, Treil and Volberg, and degenerate Sobolev spaces with matrix weights have been considered by several authors for their applications to PDEs. We prove that the classical Meyers–Serrin theorem, \(H=W\), holds in this setting. As applications we prove partial regularity results for weak solutions of degenerate p-Laplacian equations, and in particular for mappings of finite distortion.     

Thermal properties of thiocyanatocopperc(II) complexes with picolines and lutidines

The thermal properties of coordination compounds of the composition Cu(NCS)₂L₂ (whereL=pyridine, 2-, 3- and 4-picoline, and 2,3-, 2,4-, 2,5-, 2,6-, 3,4- and 3,5-lutidine) are dealt with. The thermal decomposition of these compounds begins with the release of the ligandL. The compounds with pyridine derivatives containing a methyl substituent at position 2 show a markedly decreased initial decomposition temperature. It was found that X-ray irradiation caused a reduction of the central atom Cu(II) in the coordination compounds under investigation. X-ray electron spectra data showed the stability of the compounds Cu(NCS)₂L₂ withL=picoline or lutidine having a methyl substituent at position 2 to be distinctly lower in the surface layers. From the given series, the compounds Cu(NCS)₂(pyridine)₂ and Cu(NCS)₂(3,5-lutidine)₂ exhibit an analogous course of thermal decomposition in nitrogen atmosphere up to 600°. The stoichiometries of thermal decomposition are discussed.

---

Zusammenfassung Der Artikel befaßt sich mit den thermischen Eigenschaften von Koordi-nationsverbindungen der Zusammensetzung Cu(NCS)₂ L ₂ (L= Pyridin, 2-, 3-, 4-Pikolin, 2,3-, 2.4-, 2,5-, 2,6-, 3,4- und 3,5-Lutidin). Die thermische Zersetzung dieser Verbindungen beginnt mit der Abspaltung des LigandenL. Die Verbindungen mit Pyridinderivaten, welche einen Methylsubstituenten in Position 2 im Pyridinring enthalten, zeigen eine deutlich herabgesetzte anfängliche Zersetzungstemperatur. Es wurde gefunden, daß die Röntgenbestrahlung eine Reduktion des zentralen Cu(II)-Atoms bei den untersuchten Koordinationsverbindungen herbeiführte. Die Daten der Röntgen-Elektronenspektren zeigten, daß die Stabilität der Verbindungen Cu(NCS)₂L₂ mitL=Pikolin oder Lutidin, welche einen Methylsubstituenten in Position 2 enthalten, in den Oberflächenschichten wesentlich geringer ist. Von der gegebenen Reihe der Verbindungen zeigen Cu(NCS)₂(Pyridin)₂ und Cu(NCS)₂(3,5-Lutidin)₂ in Stickstoff-Atmosphäre bis zu 600° einen ähnlichen Verlauf der thermischen Zersetzung. Die Stöchiometrie ihrer thermischen Zersetzung wird beschrieben.

---

Résumé L'article a trait aux propriétés thermiques des composés de coordination de composition Cu(SCN)₂L₂ (L=pyridine, 2-, 3-, 4-picoline, 2,3-, 2,4-, 2,5-, 2,6-, 3,4-, 3,5-lutidine). La décomposition thermique de ces composés commence avec la libération du ligandL. Les composés avec des dérivés de la pyridine contenant un substituant méthyle en position 2 sur le cycle de la pyridine présentent une température initiale de décomposition qui se trouve abaissée de manière appréciable. On observe que le traitement aux rayons X provoque une réduction de l'atome central Cu(II) dans les composés de coordination étudiés. Les données fournies par les spectres électroniques des rayons X ont montré que la stabilité des composés Cu(SCN)₂L₂ avecL= picoline ou lutidine, ayant un substituant méthyle en position 2, est nettement plus faible dans les couches superficielles. Dans cette série de composés, Cu(SCN)₂ (pyridine)₂ et Cu(SCN)₂(3,5-lutidine)₂ montrent, en atmosphère d'azote, jusqu'à 600°, un processus analogue de décomposition thermique. La stoechiométrie de leur réaction de décomposition thermique est examinée.

---

Cu(NCS)₂L₂ L=, 2-, 3-, 4- , 2,3-, 2,4-, 2,5-, 2,6-, 3,4-, 3,5-. L. 2- . , , Cu(II). , Cu(NCS)₂L₂ c L= , 2, . Cu(NCS)₂ ( )₂ Cu(NCS)₂ (3,5-)₂ 600°. .

     

Sharp weighted bounds without testing or extrapolation

We give a short proof of the sharp weighted bound for sparse operators that holds for all p,1?<?p?< ??. By recent developments this implies the bounds hold for any Calderón?CZygmund operator. The novelty of our approach is that we avoid two techniques that are present in other proofs: two weight inequalities and extrapolation. Our techniques are applicable to fractional integral operators as well.